Which of the following are correct expression for torque acting on a body?
A. \(\vec{\tau}=\vec{r}\times\vec{L}\)
B. \(\vec{\tau}=\frac{\mathrm{d}}{\mathrm{dt}}(\overrightarrow{\mathrm{r}} \times \overrightarrow{\mathrm{p}})\)
C. \(\vec{\tau}=\overrightarrow{\mathrm{r}} \times \frac{\mathrm{d} \mathrm{p}}{\mathrm{dt}}\)
D. \(\vec{\tau}=\mathrm{I} \vec{\alpha}\)
E. \(\vec{\tau}=\overrightarrow{\mathrm{r}} \times \overrightarrow{\mathrm{F}}\)
( \(\overrightarrow{\mathrm{r}}=\) position vector; \(\overrightarrow{\mathrm{p}}=\) linear momentum;
\(\overrightarrow{\mathrm{L}}=\) angular momentum; \(\vec{\alpha}=\) angular acceleration;
\(I=\) moment of inertia; \(\vec{F}=\) force; \(t=\) time)
Choose the correct answer from the options given below :

Identify the correct statements :
A. Electrostatic field lines form closed loops.
B. The electric field lines point radially outward when charge is greater than zero.
C. The Gauss-Law is valid only for inverse-square force.
D. The workdone in moving a charged particle in a static electric field around a closed path is zero.
E. The motion of a particle under Coulomb's force must take place in a plane.
Choose the correct answer from the options given below :

Which of the following statement is not true about stopping potential \(\left(\mathrm{V}_0\right)\)?

Two point charges \(A\) and \(B\) of magnitude \(+8 \times 10^{-6}\,C\) and \(-8 \times 10^{-6}\,C\) respectively are placed at a distance \(d\) apart. The electric field at the middle point \(O\) between the charges is \(6.4 \times 10^{4}\,NC ^{-1}\). The distance ' \(d\) ' between the point charges \(A\) and \(B\) is..............\(m\)

Escape velocity of a body from earth is \(11.2 \mathrm{~km} / \mathrm{s}\). If the radius of a planet be one-third the radius of earth and mass be one-sixth that of earth, the escape velocity from the plate is _______.

A resistance is shown in the figure. Its value and tolerance are given respectively by

The position vectors of two 1 kg particles, (A) and (B), are given by
\(\overrightarrow{\mathrm{r}}_{\mathrm{A}}=\left(\alpha_1 \mathrm{t}^2 \hat{i}+\alpha_2 \mathrm{t} \hat{j}+\alpha_3 \mathrm{t} \hat{k}\right) \mathrm{m}\) and \(\overrightarrow{\mathrm{r}}_{\mathrm{B}}=(\beta_1 \mathrm{t} \hat{i}+\beta_2 \mathrm{t}^2 \hat{j}\) \(+\beta_3 \mathrm{t} \hat{k}) \mathrm{m}\), respectively; \((\alpha_1=1 \mathrm{~m} / \mathrm{s}^2, \alpha_2=3 \mathrm{n} \mathrm{m} / \mathrm{s},\) \(\alpha_3=2 \mathrm{~m} / \mathrm{s},\) \(\beta_1=2 \mathrm{~m} / \mathrm{s}, \beta_2=-1 \mathrm{~m} / \mathrm{s}^2, \beta_3=4 \mathrm{pm} / \mathrm{s})\), where t is time, n and p are constants. At \(t=1 \mathrm{~s},\left|\overrightarrow{V_A}\right|=\left|\vec{V}_B\right|\) and velocities \(\vec{V}_A\) and \(\vec{V}_B\) of the particles are orthogonal to each other. At \(t=1 \mathrm{~s}\), the magnitude of angular momentum of particle (A) with respect to the position of particle (B) is \(\sqrt{\mathrm{L}} \mathrm{kgm}^2 \mathrm{~s}^{-1}\). The value of L is _______ .

A material has Poisson's ratio \(0.50.\) If a uniform rod of it suffers a longitudinal strain of \(2 \times {10^{ - 3}}\), then the percentage change in volume is

If \(\lambda \) be the ratio of the roots of the quadratic equation in \(x, 3m^2x^2 + m(m -4)x + 2 = 0\), then the least value of \(m\) for which \(\lambda  + \frac{1}{\lambda } = 1\), is

The vernier constant of Vernier callipers is \(0.1 \,mm\) and it has zero error of \((-0.05) \,cm\). While measuring diameter of a sphere, the main scale reading is \(1.7 \,cm\) and coinciding vernier division is \(5\). The corrected diameter will be ........... \(\times 10^{-2} \,cm\)

A cylindrical block of wood (density \(= 650\, kg\, m^{-3}\)), of base area \(30\,cm^2\) and height \(54\, cm\), floats in a liquid of density \(900\, kg\, m^{-3}\) . The block is depressed slightly and then released. The time period of the resulting oscillations of the block would be equal to that of a simple pendulum of length ..... \(cm\) (nearly)

A solid sphere of mass \(‘M’\) and radius \(‘a’\) is surrounded by a uniform concentric spherical shell of thickness \(2a\) and mass \(2M.\) The gravitational field at distance \(‘3a’\) from the centre will be

Consider two solid spheres of radii \(\mathrm{R}_{1}=1 \;\mathrm{m}\) \(\mathrm{R}_{2}=2\; \mathrm{m}\) and masses \(\mathrm{M}_{1}\) and \(\mathrm{M}_{2},\) respectively. The gravitational field due to sphere \((1)\) and \((2)\) are shown. The value of \(\frac{\mathrm{M}_{1}}{\mathrm{M}_{2}}\) is